Question

Find the point of intersection of the plane $\overline{r}.(1,1,1)=2$ and the line $\overline{r}=(4,5,3)+k(2,2,1),k\in R$

Answer 1

Any point on the line $\overline{r}=(4,5,3)+k(2,21)$ is given by $(4+2k,5+2k,3+k)$

Since, this point also lies on the plane given by $\overline{r}.(1,1,1)=2$

$⟹4+2k+5+2k+3+k=2$

$⟹5k=-10$

$⟹k=-2$

hence, point is $(0,1,1)$